Partition-level fusion induced multi-view Subspace Clustering with Tensorial Geman Rank.

The tensor-based multi-view clustering approach captures the high-order correlation among different views by learning a low-rank representation tensor, which has achieved favorable performance in multi-view clustering. However, the tensor rank approximation functions used by the extant algorithms are not tight enough to the true rank of the tensor, leading to the undesired low-rank structure. Besides, the fusion strategy at the affinity matrix level is less robust to noise, resulting in sub-optimal clustering results. To tackle these issues, we propose a Partition-Level Fusion Induced Multi-view Subspace Clustering with Tensorial Geman Rank (PFMSC-TGR). Firstly, a tighter surrogate of tensor rank is designed, named Tensorial Geman Rank (TGR). Under the constraint of TGR, all non-zero singular values are penalized with suitable strength, leading to a strongly discriminative representation tensor. Secondly, we fuse the information of all views at the partition level to obtain a consistent indicator matrix, which enhances the stability of the model against noisy information. Furthermore, we combine these two items in a unified framework and employ an efficient algorithm to optimize the objective function. We further mathematically prove that the sequences constructed by our proposed algorithm converge to the stationary KKT point. Extensive experiments are conducted on nine data sets with different types and sizes, and the results of comparison with the eleven state-of-the-art algorithms prove the superiority of our algorithm. Our code is publicly available at: https://github.com/jijintian/PFMSC-TGR.